\( f(x)=\displaystyle \int \dfrac{7x^{10}+9x^{8}}{(1+x^{2}+2x^{9})^{2}} \, dx,\ x>0, \ \lim_{x\to 0} f(x)=0 \) and \( f(1)=\dfrac{1}{4} \). 
. and \( B=\operatorname{adj}(\operatorname{adj}A) \) be such that \( |B|=81 \), then \( \alpha^{2} \) is equal to:
